Entropy of irregular points for some dynamical systems
Katrin Gelfert, Maria Jose Pacifico, Diego Sanhueza
TL;DR
This paper establishes conditions under which certain dynamical systems have irregular points with full topological entropy, verified for specific nonuniformly hyperbolic systems like surface diffeomorphisms and rational functions.
Contribution
It provides new sufficient conditions for the existence of irregular points with full entropy in nonuniformly hyperbolic systems.
Findings
Irregular points can have full topological entropy under certain conditions.
Conditions verified for positive entropy surface diffeomorphisms.
Conditions verified for rational functions on the Riemann sphere.
Abstract
We derive sufficient conditions for a dynamical systems to have a set of irregular points with full topological entropy. Such conditions are verified for some nonuniformly hyperbolic systems such as positive entropy surface diffeomorphisms and rational functions on the Riemann sphere.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Analytic and geometric function theory · Quantum chaos and dynamical systems